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Journal of Pure and Applied Mathematics

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The Collatz Conjecture - From 1 To Infinity, No Loops, No Gaps, No Instability, P Vs NP, Halting Problem

Author(s): Barbara Clarke*

This paper describes the derivation of three functions that when used together generate all Collatz conjecture sequences starting from 1. Three functions are necessary as will become evident. The tree structure that is defined by the functions is fractal in nature and not like any other tree structure I have seen presented (Utube). Irrespective of issues of proof the definition of data structure has the potential to significantly impact current studies of the Collatz Conjecture. The work stands alone. There are no reference papers or associated organisations. The mathematics involved do not follow the general approach used by most mathematicians, in fact nothing more difficult than high school algebra is required. Even so the paper addresses the issues of potential loops, possible gaps and the question of possible instability. The P vs NP question and halting issues for computer searches are touched on. Potentially the major impact of this work is the implication that hailstone data sets are the outcome of several functions rather than the product of a single function. Two of the functions referred to above are closely related. The third is not

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